Trips of less than three to five miles will probably be quicker by bike. So it looks like it’s worth the try. And besides that bicycling to work can be part of your daily minutes of activity, so vital for your health.
You can start by riding your route on a weekend in order to find the easiest and safest way and also clock the distance. This will give you less stress in your first working morning on the bike.
Some never start because they feel they would not be able to ride in the morning and also be fit to get back at the end of the day. If you are bothered by that, try riding to work and taking mass transit home in the evening and then alternating the next day. Pack clothes with you if you need to change.